Angle sensing in an off-axis configuration

ABSTRACT

A system may include a magnet fixed to a rotatable object. The rotatable object may be positioned to concentrically rotate about an axis. The system may also include a magnetic angle sensor configured to determine a rotation angle of the rotatable object based on a rotating magnetic field produced by the magnet and sensed by the magnetic angle sensor. The rotating magnetic field may have a radial component and a tangential component, and the magnetic angle sensor may be positioned at a sensor position having a non-zero radial distance from the axis. At the sensor position, an amplitude of the radial component may substantially match an amplitude of the tangential component, or the radial component and the tangential component may share a substantially same gradient magnitude.

BACKGROUND

A magnetic angle sensor may be used to determine an orientation of amagnetic field (e.g., between zero degrees and three hundred and sixtydegrees) produced by a magnet. The magnetic angle sensor may use giantmagnetoresistance (GMR) technology, anisotropic magnetoresistance (AMR)technology, tunnel magnetoresistance (TMR) technology, or the like.

SUMMARY

According to some possible implementations, a system may include amagnet fixed to a rotatable object, where the rotatable object may beingpositioned to concentrically rotate about an axis; and a magnetic anglesensor configured to determine a rotation angle of the rotatable objectbased on a rotating magnetic field produced by the magnet and sensed bythe magnetic angle sensor, where the rotating magnetic field may have aradial component and a tangential component, where the magnetic anglesensor may be positioned at a sensor position having a non-zero radialdistance from the axis, and where, at the sensor position, an amplitudeof the radial component may substantially match an amplitude of thetangential component, or at the sensor position, the radial componentand the tangential component may share a substantially same gradientmagnitude.

According to some possible implementations, a magnetic angle sensor mayinclude one or more sensor components configured to: determine, based ona rotating magnetic field produced by a magnet, a rotation angle of themagnet during a substantially concentric rotation of the magnet with arotatable object, where the rotatable object may be positioned tosubstantially concentrically rotate about an axis, where the rotatingmagnetic field may have a radial component and a tangential component,and where the magnetic angle sensor may be positioned at a sensorposition having a non-zero radial distance from the axis, where anamplitude of the radial component may substantially match an amplitudeof the tangential component at the sensor position.

According to some possible implementations, a magnetic angle sensor mayinclude one or more sensor components configured to: determine, based ona rotating magnetic field produced by a magnet, a rotation angle of themagnet during a substantially concentric rotation of the magnetconnected to a rotatable object, where the rotatable object may bepositioned to substantially concentrically rotate about an axis, wherethe rotating magnetic field may have a radial component and a tangentialcomponent, and where the magnetic angle sensor may be positioned at asensor position having a non-zero radial distance from the axis, wherethe radial component and the tangential component may share asubstantially same gradient magnitude at the sensor position.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of an overview of an example implementationdescribed herein;

FIGS. 2A and 2B are diagrams of an example environment in whichapparatuses described herein may be implemented;

FIG. 3 is a diagram of example components of an angle sensor included inthe example environment of FIGS. 2A and 2B;

FIGS. 4A and 4B include graphical representations that show examples ofhow placing an angle sensor in an off-axis position, relative to amagnet that produces a magnetic field, may introduce non-linearities tothe magnetic field as experienced by the angle sensor;

FIGS. 5A-5D are diagrams of an example implementation relating tooff-axis positioning of an angle sensor, as described herein.

DETAILED DESCRIPTION

The following detailed description of example implementations refers tothe accompanying drawings. The same reference numbers in differentdrawings may identify the same or similar elements.

An angle sensor may be configured to sense one or more components of arotating magnetic field. The rotating magnetic field may be generated bya magnet rotating about an axis (e.g., an axis passing through a centerof a rotatable object). Conveniently, the magnet may be rotatingconcentrically with the rotatable object. It is assumed for theremainder of this disclosure that the magnet follows the rotationalmovement of the rotatable object (i.e., that the magnet rotates aboutthe axis in correspondence to the rotatable object). This may beachieved by providing a connection (e.g., a mechanical connection)between the magnet and the rotatable object. Based on the rotatingmagnetic field, more precisely on the one or more components of therotating magnetic field, a rotation angle of the rotatable object may bedetermined. (e.g., with respect to a reference angle). Assuming non-slipbetween the magnet and the rotatable object, the angle of the magnetcorresponds to the rotational angle of the rotatable object.

The angle sensor may be configured to sense a radial component of themagnetic field (e.g., a component of the magnetic field in a directioncorresponding to a radius of the magnet) and a tangential component ofthe magnetic field (e.g., a component of the magnetic field in adirection corresponding to a tangent of the magnet and substantiallyorthogonal to the radial component of the magnetic field). Here, theangle sensor may determine the rotation angle of the magnet, and hencethe rotatable object, based on the radial component of the rotatingmagnetic field and the tangential component of the rotating magneticfield.

In some cases, the angle sensor may be positioned along the axis ofrotation of the magnet and the rotatable object (herein referred to as“on-axis”). In other words, the angle sensor may be placed at a positionon the axis of rotation at an axial distance from the center of themagnet. For the remainder of this disclosure it shall be assumed thatthe axis of rotation extends beyond the length of the rotatable object.Therefore, a sensor position along an extension of the axis of rotationbeyond the actual length of the rotatable object shall also be referredto as an “on-axis” position.

When placed in an on-axis position, the angle sensor may be capable ofaccurately determining the rotation angle of the magnet and/or may berobust against one or more positioning tolerances, such as an assemblytolerance, a dynamic change in positioning (e.g., due to vibration), orthe like.

However, in some scenarios, it may not be possible to place the anglesensor in an on-axis position (e.g., due to spacing limitations, due tomovement of the rotatable object in another direction with respect tothe angle sensor, such as a vertical direction, a horizontal direction,etc.). Therefore, in such a case, the angle sensor may be placed at aposition at a radial distance from the axis of rotation (herein referredto as “off-axis”). A person of ordinary skill will appreciate that theradial distance will typically be larger than the radius of therotatable object. Such off-axis positioning of the angle sensor mayintroduce non-linearities to the magnetic field as sensed by the anglesensor, which may necessitate end-of-line (EOL) calibration of the anglesensor and/or may reduce robustness of the angle sensor against staticpositioning tolerances, dynamic positioning tolerances, or the like,such that the possibility of an angle error, in a determination of therotation angle may be increased (e.g., as compared to placement of theangle sensor at an on-axis position).

Implementations described herein may relate to placing an angle sensorat a first off-axis position, relative to a magnet, such that anamplitude of a radial component of a rotating magnetic field, producedby the magnet, substantially matches an amplitude of a tangentialcomponent of the rotating magnetic field. In some implementations,placing the angle sensor at the first off-axis position may eliminate aneed for EOL calibration of the angle sensor.

Implementations described herein may further relate to placing the anglesensor at a second off-axis position such that a gradient magnitude ofthe radial component of the rotating magnetic field is substantially thesame as a gradient magnitude of the tangential component of the rotatingmagnetic field. In some implementations, placing the angle sensor at thesecond off-axis position may increase robustness of the angle sensoragainst a static positioning tolerance, a dynamic positioning tolerance,or the like.

FIG. 1 is a diagram of an overview of an example implementation 100described herein. For the purpose of example implementation 100, assumethat a magnet is connected to a rotatable object (shown in across-sectional view in FIG. 1), and that the rotatable objectconcentrically rotates around an axis at the center of the rotatableobject. Typically, the magnet is mounted fixedly on the rotatable objectin order to follow the rotational movement of the rotatable object. Thisis to say that the rotation of the magnet represents or corresponds tothe rotational movement of the rotatable object about the axis. Notably,while the magnet is depicted as circular or annular, in someimplementations, the magnet may be of another form, including ellipticalbut also of non-rotational symmetry. Due to the rotation of therotatable magnet about the axis, the magnet will produce a rotatingmagnetic field as the magnet comprises more than one north pole (N) andsouth pole (S) that will move relative to a given position of an anglesensor (e.g., in an on-axis or an off-axis position). Further, assumethat an angle sensor is capable of sensing a radial component and atangential component of the magnetic field in order to determine arotation angle of the magnet with respect to a reference direction, andhence the rotational angle of the rotatable object. Finally, assume thatthe angle sensor may not be placed in an on-axis position (e.g., due toa spacing limitation, due to movement of the magnet in a direction,etc.).

As shown in the left portion of FIG. 1, the angle sensor may be placedat a first position (e.g., position 1) that is at a first radialdistance (e.g., distance 1) from the axis about which the rotatableobject, and the magnet, rotate. As noted in the right portion of FIG. 1,placing the angle sensor at the first radial distance from the axis ofrotation may cause an amplitude of the radial component of the magneticfield to substantially match (i.e., be approximately equal to) anamplitude of a tangential component of the magnetic field. As furthernoted, placing the angle sensor at the first radial distance from theaxis of rotation may eliminate a need for EOL calibration of the anglesensor.

As further shown in the left portion of FIG. 1, the angle sensor mayalternatively be placed at a second position (e.g., position 2) that isat a second radial distance (e.g., distance 2) from the axis of rotationof the magnet. As further noted in the right portion of FIG. 1, placingthe angle sensor at the second radial distance from the axis of rotationmay cause a gradient magnitude of the radial component of the magneticfield to be substantially the same as (i.e., be approximately equal to)a gradient magnitude of the tangential component of the magnetic field.As noted, placing the angle sensor at the second radial distance mayincrease robustness of the angle sensor against one or more positioningtolerances associated with the angle sensor, such as a staticpositioning tolerance (e.g., an assembly tolerance), a dynamictolerance, or the like.

In this way, the angle sensor may be placed at an off-axis location suchthat operation of the angle sensor may be improved (e.g., by notrequiring EOL calibration, by being robust against one or morepositioning tolerances, etc.).

FIGS. 2A and 2B are diagrams of example environments 200 in whichapparatuses described herein may be implemented. As shown in FIG. 2A,environment 200 may include a rotatable object 205, a magnet 210, anangle sensor 220, and a controller 230.

Rotatable object 205 may include an object positioned to concentricallyrotate about axis 215. For example, rotatable object 205 may include arotational component of a combustion engine, such as a crank shaft, acam shaft, or the like. In some implementations, rotatable object 205may be connected (e.g., mechanically) to magnet 210 such that a rotationangle of magnet 210 corresponds to a rotation angle of rotatable object205.

Magnet 210 may include one or more magnets positioned to rotate withrotatable object 205 about axis 215. In the example environment 200shown in FIG. 2A, magnet 210 comprises a first half forming a north pole(N) and a second half forming a south pole (S), so that magnet 210comprises one pole pair. A person of ordinary skill will appreciate thatmagnet 210 may, without limitation, comprise more than one pole pair inanother implementation. In some implementations, magnet 210 may includea ring magnet that is positioned concentrically about axis 215 thatpasses through the center of rotatable object 205 and magnet 210, asshown in the cross-sectional view of FIG. 2A. While magnet 210 is shownas circular in FIG. 2A, magnet 210 may be of elliptical shape in aninstance in which an angle between a ring plane and axis 215 deviatesfrom a substantially perpendicular relation. The ring plane is a planesymmetrically cutting through magnet 210 and includes the magnet center.In most practical cases, the ring plane may be substantiallyperpendicular to axis 215. As another example, magnet 210 may include adisk magnet that is positioned to rotate with rotatable object 205 aboutaxis 215. A disk magnet may be of interest for an arrangement of magnet210 at an end of rotatable object 205 (not shown). Rotation of rotatableobject 205 will correspond to rotation of the disk magnet provided thereis a non-slip relation between an end face of rotatable object 205 andthe disk magnet.

As yet another example, magnet 210 may include a magnet of anothershape, that is positioned to rotate with rotatable object 205 about axis215. In some implementations, magnet 210 may include two alternatingpoles on two portions of magnet 210 (e.g., a north pole on a first halfof magnet 210, a south pole on a second half of magnet 210).Additionally, or alternatively, magnet 210 may include a dipole magnet(e.g., a dipole bar magnet, a circular dipole magnet, an ellipticaldipole magnet, etc.), a permanent magnet, an electromagnet, a magnetictape, or the like. Magnet 210 may be comprised of a ferromagneticmaterial (e.g., Hard Ferrite), and may produce a magnetic field. Magnet210 may further comprise a rare earth magnet which may be of advantagedue to an intrinsically high magnetic field strength of rare earthmagnets. As described above, in some implementations, magnet 210 may beattached to or coupled with rotatable object 205 for which a rotationangle is to be measured by angle sensor 220.

Angle sensor 220 may include one or more apparatuses for detectingcomponents of a magnetic field for use in determining an angle ofrotation of magnet 210. For example, angle sensor 220 may include one ormore circuits (e.g., one or more integrated circuits). In someimplementations, angle sensor 220 may be placed at a position relativeto magnet 210 such that angle sensor 220 may detect components of amagnetic field generated by magnet 210.

In some implementations, angle sensor 220 may include two or moresensing elements configured to sense an amplitude of a component of amagnetic field present at angle sensor 220 by magnet 210, such as aradial component of the rotating magnetic field, a tangential componentof the rotating magnetic field, or the like.

For example, the first and second sensing element of the angle sensor220 may be implemented as a single half bridge as known to a person ofordinary skill in the art. The first sensing element of the half bridgemay be configured to sense the radial component of the rotating magneticfield, while the second sensing element of the half bridge may beconfigured to sense the tangential component of the rotating magneticfield at the position of the respective sensing elements. It will beappreciated that the angle sensor 220 employing the single half bridgeonly, will not be able to unambiguously detect an angular position atstart-up. Instead, a second measurement will be required to resolve theambiguity inherent to half bridges.

Alternatively, angle sensor 220 may implement the first sensing elementas a first sensor half bridge configured to sense an amplitude of theradial component of the rotating magnetic field generated by magnet 210at the position of the first sensor bridge, and a second sensor halfbridge configured to sense an amplitude of the tangential component ofthe magnetic field produced by magnet 210 at the position of the secondsensor half bridge. The use of first and second sensor half bridges isof interest for applications in which a start-up angular position isrequired and it is not practical to take a second reading in order toestablish the current angular position. Such limitations apply tocamshaft or crankshaft angle sensors in vehicles but are not limitedthereto. While the first and second half bridges may provide anunambiguous start-up angular position and angular values of higheraccuracy as compared to the single half bridge angle sensor, as atrade-off, angle sensor 220 comprising half bridges as sensing elementsmay be more expensive, now comprising four magnetoresistive elementsrather than two as for the single half bridge angle sensor 220. Forangle sensor 220 implemented using two half bridges as sensing elements,each sensing element is configured to output two output signals (typicalsine and cosine signals) corresponding to the amplitude of the componentof the magnetic field at the position of the respective half bridge. Insome implementations, the two or more output signals may be used (e.g.,by angle sensor 220 and/or controller 230) to determine a rotation angleof magnet 210, and hence the rotation angle of rotatable object 205.

As a further alternative, a full bridge (e.g., a Wheatstone bridge) maybe used as the first sensing element, and a second full bridge may beused as the second sensing element in order to determine an amplitude ofthe radial component and the tangential component of the rotatingmagnetic field, respectively. Using the full bridge as first and secondsensing element will improve accuracy of the determined radial andtangential components over those values determined using half bridges asindividual sensing elements or the one half bridge only comprising bothfirst and second sensing element. As a trade-off, angle sensor 220employing two full bridges will be more expensive and require more spacewithin an integrated circuit.

In some implementations, the integrated circuit may include anintegrated controller 230 (e.g., such that an output of angle sensor 220may include information that describes a rotation angle of magnet 210and rotatable object 205). Additional details regarding angle sensor 220are described below with regard to FIG. 3.

FIG. 2A shows a cross-sectional view of an example environment 200. Asshown in FIG. 2A, in some implementations, angle sensor 220 may beplaced at a radial distance (e.g., d_(R)) from an axis of rotation ofmagnet 210. In some implementations, the radial distance may be lessthan an outer radius of magnet 210 (e.g., R). If the radial distanced_(R) is less than or equal to the outer radius R, angle sensor 220should be positioned at a position beyond an end face of rotatableobject 205, in order not to intersect with rotatable object 205. In someimplementations, the radial distance may be greater than the radius ofmagnet 210, such as a distance that is approximately two times theradius of magnet 210. In some implementations, the radial distance atwhich angle sensor 220 is placed may correspond to a position at whichan amplitude of a radial component of the rotating magnetic field,produced by magnet 210 and sensed by angle sensor 220, substantiallymatches an amplitude of a tangential component of the rotating magneticfield, as described in further detail below. Additionally, oralternatively, the radial distance at which angle sensor 220 is placedmay correspond to a position at which a gradient magnitude of the radialcomponent of the rotating magnetic field is substantially the same as agradient magnitude of the tangential component of the rotating magneticfield, as described in further detail below.

FIG. 2B shows a side view of example environment 200, and may correspondto the cross-sectional view of example environment 200 shown in FIG. 2A.As shown in FIG. 2B, in some implementations, angle sensor 220 may beplaced at an axial distance (e.g., d_(A)) in a direction of axis 215 andrelative to a surface of magnet 210 and rotatable object 205.

Controller 230 may include one or more circuits associated withdetermining a rotation angle of magnet 210, and providing informationassociated with the rotation angle of magnet 210 and hence the rotationangle of rotatable object 205. For example, controller 230 may includeone or more circuits (e.g., an integrated circuit, a control circuit, afeedback circuit, etc.). Controller 230 may receive input signals fromone or more sensors, such as one or more angle sensors 220, may processthe input signals (e.g., using an analog signal processor, a digitalsignal processor, etc.) to generate an output signal, and may providethe output signal to one or more other devices or systems. For example,controller 230 may receive one or more input signals from angle sensor220, and may use the one or more input signals to generate an outputsignal comprising the angular position of rotatable object 205.

The number and arrangement of apparatuses shown in FIGS. 2A and 2B areprovided as an example. In practice, there may be additionalapparatuses, fewer apparatuses, different apparatuses, or differentlyarranged apparatuses than those shown in FIGS. 2A and 2B. Furthermore,two or more apparatuses shown in FIGS. 2A and 2B may be implementedwithin a single apparatus, or a single apparatus shown in FIGS. 2A and2B may be implemented as multiple, distributed apparatuses.Additionally, or alternatively, a set of apparatuses (e.g., one or moreapparatuses) of environment 200 may perform one or more functionsdescribed as being performed by another set of apparatuses ofenvironment 200.

FIG. 3 is a diagram of example components of angle sensor 220 includedin example environment 200 of FIGS. 2A and 2B. As shown, angle sensor220 may include two or more sensing elements 310, an analog-to-digitalconvertor (ADC) 320, a digital signal processor (DSP) 330, a memorycomponent 340, and a digital interface 350.

Sensing element 310 may include one or more apparatuses for sensing anamplitude of a component of a magnetic field present at the angle sensor220 (e.g., the magnetic field generated by magnet 210). For example,sensing element 310 may include a Hall sensor that operates based on aHall-effect. As another example, sensing element 310 may include amagnetoresistance (MR) sensor, comprised of a magnetoresistive material(e.g., nickel iron (NiFe)), where the electrical resistance of themagnetoresistive material may depend on a strength and/or a direction ofthe magnetic field present at the magnetoresistive material. Here,sensing element 310 may measure magnetoresistance based on ananisotropic magnetoresistance (AMR) effect, a giant magnetoresistance(GMR) effect, a tunnel magnetoresistance (TMR) effect, or the like. Asan additional example, sensing element 310 may include a variablereluctance (VR) sensor that operates based on induction.

ADC 320 may include an analog-to-digital converter that converts ananalog signal from the one or more sensing elements 310 to a digitalsignal. For example, ADC 320 may convert analog signals, received fromthe one or more sensing elements 310, into digital signals to beprocessed by DSP 330. ADC 320 may provide the digital signals to DSP330. In some implementations, angle sensor 220 may include one or moreADCs 320.

DSP 330 may include a digital signal processing device or a collectionof digital signal processing devices. In some implementations, DSP 330may receive a digital signal from ADC 320 and may process the digitalsignal to form an output signal (e.g., destined for controller 230 bestseen in FIG. 2A or 2B), such as an output signal associated withdetermining the rotation angle of magnet 210 rotating with rotatableobject 205.

Optional memory component 340 may include a read only memory (ROM)(e.g., an EEPROM), a random access memory (RAM), and/or another type ofdynamic or static storage device (e.g., a flash memory, a magneticmemory, an optical memory, etc.) that stores information and/orinstructions for use by angle sensor 220. In some implementations,memory component 340 may store information associated with processingperformed by DSP 330. Alternatively, memory component 340 may storeconfigurational values or parameters for the two or more sensingelements 310 and/or information for one or more other components ofangle sensor 220, such as ADC 320 or digital interface 350.

Digital interface 350 may include an interface via which angle sensor220 may receive and/or provide information from and/or to anotherdevice, such as controller 230 (see FIG. 2A, 2B). For example, digitalinterface 350 may provide the output signal, determined by DSP 330, tocontroller 230 and further receive information from the controller 230.

The number and arrangement of components shown in FIG. 3 are provided asan example. In practice, angle sensor 220 may include additionalcomponents, fewer components, different components, or differentlyarranged components than those shown in FIG. 3. Additionally, oralternatively, a set of components (e.g., one or more components) ofangle sensor 220 may perform one or more functions described as beingperformed by another set of components of angle sensor 220.

FIGS. 4A and 4B include graphical representations 400 that show examplesof how placing angle sensor 220 in an off-axis position, relative tomagnet 210 that produces a magnetic field, may introduce non-linearitiesto the magnetic field present at and hence sensed by angle sensor 220.For the purposes of FIG. 4A, assume that angle sensor 220 is placed atan on-axis position relative to magnet 210.

As shown in the center portion of FIG. 4A, when angle sensor 220 isplaced in the on-axis position, a magnitude |B| of the magnetic fieldsensed by angle sensor 220 may be homogenous (i.e., constant) for anyrotation angle (shown as “mechanical angle” along the horizontaldirection) of magnet 210. For example, as shown by the “|B|” line in thecenter portion of FIG. 4A, the magnitude of the rotating magnetic field,present at angle sensor 220 for any rotation angle, is constant. Here,the rotation angle may be determined based on the radial component(e.g., “Br”) and the tangential component (e.g., “Bt”) that make up thehomogenous magnitude of the magnetic field based on the followingequation:|B|=√{square root over (B _(r) ² +B _(t) ²)}.The homogeneity of the magnitude of the magnetic field may be furtherillustrated by the intersection of the radial component and thetangential component at a 45° rotation angle (shown by the arrow on thecenter portion of FIG. 4A). In other words, a homogenous magnetic fieldwould cause the radial component and the tangential component to beequal at a 45° rotation angle.

The homogeneity of the magnitude of the rotating magnetic field may alsobe illustrated by the circular shape of the plot in the left portion ofFIG. 4A. As shown, plotting the tangential component Bt over the radialcomponent Br yields the circular shape provided that there are nofurther effects affecting the magnetic field components Br and Bt, suchas variations in position of angle sensor 220 or off-set errors ofindividual sensing elements 310 of angle sensor 220, as known to aperson of ordinary skill in the art.

As shown by the right portion of FIG. 4A, due to the homogeneity of themagnitude of magnetic field |B|, the direction of the magnetic fieldsensed by the angle sensor 220 may have a linear non-ambiguousrelationship with respect to the rotation angle of magnet 210. In otherwords, the direction of the rotating magnetic field sensed by anglesensor 220 may vary linearly with respect to the rotation angle ofmagnet 210, for an on-axis positioning of the angle sensor 220. In sucha case, EOL calibration may not be needed and/or angle sensor 220 may berobust against a positioning tolerance, such as an assembly tolerance, adynamic tolerance due to vibration, or the like. However, when anglesensor 220 is placed at an off-axis position, non-linearities may beintroduced to the magnetic field present at angle sensor 220, asdescribed below with respect to FIG. 4B.

For the purposes of FIG. 4B, assume that angle sensor 220 is placed atan off-axis position relative to magnet 210, as shown in FIG. 2A as anon-limiting example. As shown in the center portion of FIG. 4B, whenangle sensor 220 is placed in the off-axis position, the magnitude ofrotating magnetic field |B| sensed by angle sensor 220 may not behomogenous (i.e., may not be constant) for different rotation angles(shown as “mechanical angle”) of magnet 210. For example, as shown bythe “|B|” line in the center portion of FIG. 4B, the magnitude of therotating magnetic field sensed by angle sensor 220 for various rotationangles of magnet 210, may not be constant as sensed by angle sensor 220.As such, a rotation angle determined based on the radial component(e.g., “Br”) and the tangential component (e.g., “Bt”) that make up thenon-homogenous magnitude of the rotating magnetic field according to theabove formula, may not accurately represent the rotation angle of magnet210 (e.g., the rotation angle may include an angle error). Thenon-homogeneity of the magnitude of the magnetic field may be furtherillustrated by the inequality of the radial component and the tangentialcomponent at a 45° rotation angle (shown by the arrow on the centerportion of FIG. 4B). In other words, a non-homogenous magnetic fieldwould cause the radial component and the tangential component to differat a 45° rotation angle.

The non-homogeneity of the magnetic field may also be illustrated by theelliptical shape of the plot on the left portion of FIG. 4B. As shown,plotting the tangential component Bt over the radial component Br yieldsthe elliptical shape provided that there are no further effectsaffecting the magnetic field components Br and Bt, such as variations inposition of angle sensor 220 or off-set errors of individual sensingelements 310, as known to a person of ordinary skill in the art

As shown by the right portion of FIG. 4B, due to the non-homogeneity ofthe magnitude of the rotating magnetic field sensed by the angle sensor220, the direction of the magnetic field may not have a linearrelationship with respect to the rotation angle of magnet 210 and hencerotatable object 205. In other words, the direction of the magneticfield sensed by angle sensor 220 may not vary linearly with respect tothe rotation angle of magnet 210. As such, EOL calibration of anglesensor 220 may be needed. Furthermore, the off-axis positioning of anglesensor 220 may reduce a robustness of angle sensor 220 againstpositioning tolerances.

However, as described below, angle sensor 220 may be placed at a firstoff-axis position such that EOL calibration may not be necessary.Alternatively, as described below, angle sensor 220 may be placed at asecond off-axis position such that angle sensor 220 is robust againstpositioning tolerances.

As indicated above, FIGS. 4A and 4B are provided merely as examples.Other examples are possible and may differ from what was described withregard to FIGS. 4A and 4B.

FIGS. 5A-5D are diagrams of an example implementation 500 relating tooff-axis positioning of angle sensor 220, as described herein. For thepurposes of example implementation 500, assume magnet 210 is connectedto rotatable object 205 that is positioned to concentrically rotateabout axis 215. Further, assume that angle sensor 220 is to be placed atan off-axis position relative to axis 215 about which rotatable object205 concentrically rotates. For example, angle sensor 220 may be placedin an off-axis position due to a spacing limitation. As another example,angle sensor 220 may be placed in an off-axis position due to a possiblemovement of rotatable object (and magnet 210) in another direction, suchas a vertical direction relative to angle sensor 220, a horizontaldirection relative to angle sensor 220, or the like.

As shown in a cross-sectional view in the left portion of FIG. 5A,magnet 210 may include a ring magnet with an inner radius of 7millimeters (mm) and an outer radius of 12 mm. Let us further assumethat angle sensor 220 is to be placed at an axial distance (e.g., adistance in axial direction from a surface of magnet 210 and rotatableobject 205) of 3 mm, best seen in the side view in the right portion ofFIG. 5B. Here, it may be desirable to place angle sensor 220 at a firstposition corresponding to a first radial distance (e.g., d_(R1)) fromthe axis of rotation, such that EOL calibration of angle sensor 220 isnot needed, or at a second position corresponding to a second radialdistance from the axis of rotation (e.g., d_(R2)) such that angle sensor220 is robust against one or more positioning tolerances.

FIG. 5B is a graphical representation associated with identifying anoff-axis position for angle sensor 220 in order to eliminate a need forEOL calibration or to increase robustness of angle sensor 220 against apositioning tolerance. As shown, in some implementations, the firstradial distance and the second radial distance may be determined basedon comparing a radial component of a rotating magnetic field generatedby magnet 210 and a tangential component of the rotating magnetic fieldgenerated by magnet 210 across a range of radial distances at arespective radial position of the angle sensor 220. For an examplemagnet, the radial component (solid points in FIG. 5B) of the rotatingmagnetic field and the tangential component (open squares in FIG. 5B) ofthe rotating magnetic field are plotted for a radial distance rangingfrom 0 mm to 35 mm in FIG. 5B. The radial component and the tangentialcomponent may vary across the range of radial distances (e.g., betweenapproximately −140 milliteslas (mT) and approximately 50 mT).

Here, the first position, corresponding to the first radial distanceassociated with eliminating a need for EOL calibration, may beidentified by a radial distance at which the amplitude of radialcomponent of the magnetic field substantially matches (e.g., within 1%,within 5%, within 10%, etc.) the amplitude of the tangential componentof the magnetic field. In this example, the first position may beidentified as a position with a radial distance of approximately 11.8 mmfrom the axis of rotation (e.g., identified by the shaded areacorresponding to point 1). Here, if angle sensor 220 is placed at aradial distance of 11.8 from the axis of rotation of magnet 210, theamplitude of the radial component of the magnetic field maysubstantially match the tangential component of the magnetic field. Assuch, a need for EOL calibration of angle sensor 220 may be eliminatedwhen angle sensor 220 is placed 11.8 mm from the axis of rotation. Here,the substantial match between the amplitude of the radial component ofthe magnetic field and the amplitude of the tangential component of themagnetic field results in a vector length (a module between the radialcomponent and the tangential component) of a substantially constantmagnitude through an entire (e.g., 360°) rotation. Therefore, an angularchange of the magnetic field direction is substantially linear to themechanical rotation of magnet 210 connected to rotatable object 205. Asthe behavior is linear, no angle error is introduced, eliminating a needfor an end-of-line calibration and/or another type of compensation.

The second position, corresponding to the second radial distanceassociated with increasing robustness against positioning tolerances,may be identified by a radial distance at which a magnitude of agradient of the radial component of the rotating magnetic field issubstantially the same as (e.g., within 1%, within 5%, within 10%, etc.)a magnitude of a gradient of the tangential component of the rotatingmagnetic field. In this example, the second position may be identifiedas a position with a radial distance of approximately 23.0 mm from theaxis of rotation (e.g., identified by the shaded area corresponding topoint 2). Here, if angle sensor 220 is placed at a radial distance of23.0 from the axis of rotation of magnet 210, the gradient magnitude ofthe radial component of the rotating magnetic field may be substantiallythe same as the gradient magnitude of the tangential component of therotating magnetic field. As such, angle sensor 220 may be robust againstone or more positioning tolerances (e.g., an assembly tolerance, adynamic tolerance, etc.) when angle sensor 220 is placed 23.0 mm fromthe axis of rotation for the illustrated example.

Notably, the second position may be identified based on a radialdistance at which the magnitudes of the gradients are substantially thesame, rather than a radial distance at which the gradients aresubstantially the same. In other words, as shown in FIG. 5B, thegradients need not have a same sign (e.g., the radial component may havepositive gradient and the tangential component may have a negativegradient).

In some implementations, as illustrated in example implementation 500,the first position may correspond to a first radial distance that isapproximately equal to a radius of magnet 210 (e.g., 12 mm≈11.8 mm).Similarly, the second position may correspond to a second radialdistance that is approximately equal to two times the radius of magnet210 (e.g., 12 mm×2≈23 mm).

In some implementations, the first radial distance and the second radialdistance may depend on one or more geometrical factors associated withmagnet 210 and/or angle sensor 220, such as an inner radius of magnet210, an outer radius of magnet 210, an axial distance at which anglesensor 220 is to be placed relative to a surface of magnet 210, or thelike. Additionally, or alternatively, the first radial distance and thesecond radial distance may depend on one or more material factorsassociated with magnet 210 and/or angle sensor 220, such as a type ofmaterial from which magnet 210 is constructed, a strength of a magneticfield produced by magnet 210, a type of angle sensor 220 (e.g.,Hall-effect, AMR, GMR, TMR, VR, etc.), or the like. In other words, thefirst radial distance and the second radial distance may vary based onone or more geometrical factors and/or material factors associated withmagnet 210 and/or angle sensor 220.

FIG. 5C is a graphical representation showing an example of robustnessof angle sensor 220 against a radial positioning tolerance of 0.3 mmwhen angle sensor 220 is placed at the second position (e.g., 23 mm).Solid symbols in FIG. 5C correspond to radial and tangential components(see left scale of FIG. 5C) of the rotating magnetic field over therotation angle at a radial position of 23 mm, corresponding to region 2of FIG. 5B. For comparison, open symbols correspond to radial andtangential components of the rotating magnetic field at a radialdistance of 23.3 mm. The radial component of the rotating magnetic fieldis illustrated as solid circle for the radial position of 23 mm, whileopen circles represent the radial component of the rotating magneticfield at the radial position of 23.3 mm. The tangential component of therotating magnetic field is illustrated as solid squares for the radialposition of 23 mm, while open squares represent the tangential componentof the rotating magnetic field at the radial position of 23.3 mm. Asshown, even with the 0.3 mm displacement in the radial direction (e.g.,due to an assembly tolerance, a vibration, a dynamic tolerance, etc.),the radial component of the magnetic field at 23.0 mm and 23.3 mm may besubstantially unchanged (best seen by comparing open and closed squaresin FIG. 5C). The tangential component of the magnetic field also remainssubstantially unchanged (best seen by comparing open and closed circlesin FIG. 5C). As further shown (e.g., by the “delta (°)” line pertainingto the right scale of FIG. 5C), an angle error between an angledetermined at the 23.0 mm radial position and the 23.3 mm radialposition may be substantially less than 1°. A person of ordinary skillin the art will appreciate that the error as displayed in FIG. 5C isdominated by some noise due to an artifact from a mesh used in thesimulation, but not a reliable representation of the angle error. Assuch, angle sensor 220, placed at the second radial position, may berobust against a positioning tolerance in the radial direction.

FIG. 5D is an example graphical representation showing robustness ofangle sensor 220 against an axial positioning tolerance of 0.3 mm whenangle sensor 220 is placed at the second position (e.g., 23 mm) and atan axial distance of 3.0 mm (i.e., the axial distance as described abovewith regard to example implementation 500). As shown, even with the 0.3mm displacement in the axial direction (e.g., due to an assemblytolerance, a vibration, a dynamic tolerance, etc.), the radial componentof the rotating magnetic field corresponding to the 3.0 mm axialdistance (solid circles in FIG. 5D) and the radial component of therotating magnetic field at the 3.3 mm axial distance (open circles inFIG. 5D) are substantially unchanged. The tangential component of therotating magnetic field may also be substantially unchanged by the 0.3mm variation in axial direction (best seen by comparing solid squaresand open squares of FIG. 5D). As further shown (e.g., by the “delta (°)”line pertaining to the right scale of FIG. 5D), an angle error betweenan angle determined at the 3.0 mm axial position and the 3.3 mm axialposition may be approximately less than 1°. Comparing the angle errorsfrom FIGS. 5C and 5D one will find there is some variation in the errorfor FIG. 5D as the error shows some kind of oscillating behavior besidesthe artifact caused by the mesh used in the simulation. As such, anglesensor 220 placed at the second position may be robust against apositioning tolerance in the axial direction.

In some implementations, axial robustness of angle sensor 220 may befurther increased with additional magnets 210. For example, if anglesensor 220 is placed between two magnets 210 configured to rotate aboutan axis, then angle error due to axial positioning tolerances may befurther reduced or even eliminated (e.g., without softwarecompensation).

As indicated above, FIGS. 5A-5D are provided merely as an example. Inother words, all radii, distances, positions, and the like, associatedwith example implementation 500 are provided merely as examples tofacilitate an understanding of how to determine beneficial off-axispositions for angle sensor 220. Other examples are possible and maydiffer from what was described with regard to FIGS. 5A-5D.

Implementations described herein may relate to placing an angle sensorat a first off-axis position, relative to a magnet, such that anamplitude of a radial component of a rotating magnetic field, producedby the magnet, substantially matches an amplitude of a tangentialcomponent of the rotating magnetic field. In some implementations,placing the angle sensor at the first off-axis position may eliminate aneed for EOL calibration of the angle sensor.

Implementations described herein may further relate to placing the anglesensor at a second off-axis position such that a gradient magnitude ofthe radial component of the rotating magnetic field is substantially thesame as a gradient magnitude of the tangential component of the rotatingmagnetic field. In some implementations, placing the angle sensor at thesecond off-axis position may increase robustness of the angle sensoragainst one or more positioning tolerances.

The foregoing disclosure provides illustration and description, but isnot intended to be exhaustive or to limit the implementations to theprecise form disclosed. Modifications and variations are possible inlight of the above disclosure or may be acquired from practice of theimplementations.

Even though particular combinations of features are recited in theclaims and/or disclosed in the specification, these combinations are notintended to limit the disclosure of possible implementations. In fact,many of these features may be combined in ways not specifically recitedin the claims and/or disclosed in the specification. Although eachdependent claim listed below may directly depend on only one claim, thedisclosure of possible implementations includes each dependent claim incombination with every other claim in the claim set.

No element, act, or instruction used herein should be construed ascritical or essential unless explicitly described as such. Also, as usedherein, the articles “a” and “an” are intended to include one or moreitems, and may be used interchangeably with “one or more.” Furthermore,as used herein, the term “set” is intended to include one or more items(e.g., related items, unrelated items, a combination of related itemsand unrelated items, etc.), and may be used interchangeably with “one ormore.” Where only one item is intended, the term “one” or similarlanguage is used. Also, as used herein, the terms “has,” “have,”“having,” or the like are intended to be open-ended terms. Further, thephrase “based on” is intended to mean “based, at least in part, on”unless explicitly stated otherwise.

What is claimed is:
 1. A system, comprising: a magnet fixed to arotatable object, the rotatable object being positioned toconcentrically rotate about an axis; and a magnetic angle sensorconfigured to determine a rotation angle of the rotatable object basedon a rotating magnetic field produced by the magnet and sensed by themagnetic angle sensor, the rotating magnetic field having a radialcomponent and a tangential component, the magnetic angle sensor beingpositioned at a sensor position having a radial distance from the axisof a least half a magnet radius of the magnet, where, the magnetic anglesensor being positioned at the sensor position based on an amplitude ofthe radial component being no more than 10% different than an amplitudeof the tangential component at the sensor position having the radialdistance from the axis of a least half the magnet radius of the magnet,or the magnetic angle sensor being positioned at the sensor positionbased on a gradient magnitude of the radial component being no more than10% different than a gradient magnitude of the tangential component atthe sensor position having the radial distance from the axis of a leasthalf the magnet radius of the magnet.
 2. The system of claim 1, wherethe radial distance from the axis is approximately equal to the magnetradius for the sensor position at which the amplitude of the radialcomponent is no more than 10% different than the amplitude of thetangential component, the magnet radius being an outer radius when themagnet is a ring magnet, or the magnet radius being a disk radius whenthe magnet is a disk magnet.
 3. The system of claim 1, where the radialdistance from the axis is approximately equal to two times the magnetradius for the sensor position at which the gradient magnitude of theradial component is no more than 10% different than the gradientmagnitude of the tangential component, the magnet radius being an outerradius when the magnet is a ring magnet, or the magnet radius being adisk radius when the magnet is a disk magnet.
 4. The system of claim 1,where the radial component and the tangential component are provided todetermine the rotation angle of the rotatable object.
 5. The system ofclaim 4, where an angle error of the determined rotation angle isapproximately less than one degree.
 6. The system of claim 1, where themagnetic angle sensor is positioned at a non-zero axial distance from asurface of the magnet.
 7. The system of claim 1, where the magneticangle sensor is configured to sense the radial component or thetangential component based on a Hall effect, a tunnel magnetoresistance(TMR) effect, a giant magnetoresistance (GMR) effect, or an anisotropicmagnetoresistance (AMR) effect.
 8. The system of claim 1, where themagnet includes a ring magnet or a disk magnet.
 9. A magnetic anglesensor, comprising: one or more sensor components configured to:determine, based on a rotating magnetic field produced by a magnet, arotation angle of the magnet during a substantially concentric rotationof the magnet with a rotatable object, the rotatable object beingpositioned to substantially concentrically rotate about an axis, therotating magnetic field having a radial component and a tangentialcomponent, and the magnetic angle sensor being positioned at a sensorposition having a non-zero radial distance from the axis, the magneticangle sensor being positioned at the sensor position based on anamplitude of the radial component being no more than 10% different thanan amplitude of the tangential component at the sensor position that isat least half a magnet radius of the magnet from the axis.
 10. Themagnetic angle sensor of claim 9, where the non-zero radial distance isapproximately equal to a radius of the magnet, the radius being an outerradius when the magnet is a ring magnet, or the radius being a diskradius when the magnet is a disk magnet.
 11. The magnetic angle sensorof claim 9, where the radial component and the tangential component areprovided to determine the rotation angle of the rotatable object. 12.The magnetic angle sensor of claim 9, where the magnetic angle sensor ispositioned at a non-zero axial distance from a surface of the magnet.13. The magnetic angle sensor of claim 9, where the one or more sensorcomponents are configured to sense the radial component or thetangential component based on a Hall effect, a tunnel magnetoresistance(TMR) effect, a giant magnetoresistance (GMR) effect, or an anisotropicmagnetoresistance (AMR) effect.
 14. The magnetic angle sensor of claim9, where the magnet is a ring magnet or a disk magnet, and the magneticangle sensor is positioned relative to the ring magnet or disk magnet.15. A method comprising: mounting a magnet fixedly to a rotatableobject, the rotatable object being positioned to concentrically rotateabout an axis; and positioning a magnetic angle sensor at a sensorposition having a non-zero radial distance from the axis, the magneticangle sensor configured to determine a rotation angle of the rotatableobject based on a rotating magnetic field produced by the magnet andsensed by the magnetic angle sensor, the rotating magnetic field havinga radial component and a tangential component, the magnetic angle sensorbeing positioned at the sensor position based on an amplitude of theradial component being no more than 10% different than an amplitude ofthe tangential component at the sensor position that is at least half amagnet radius of the magnet from the axis, or the magnetic angle sensorbeing positioned at the sensor position based on a gradient magnitude ofthe radial component being no more than 10% different than a gradientmagnitude of the tangential component at the sensor position that is atleast half the magnet radius of the magnet from the axis.